Device for the compensation of chromatic dispersion

ABSTRACT

A compensating optical fibre length having a negative chromatic dispersion slope, the compensating optical fibre having a core region surrounded by a cladding region, the cladding region defining a first ring of holes, which substantially defines, around the core region an annulus with an inner radius r1 and an outer radius r2, and at least one second ring of holes that surrounds the first ring of holes, the holes running along the compensating optical fibre longitudinally and being spaced apart from each other substantially according to a predefined pitch Λ, wherein a) r1≦λ/n≦r2 where n is the refractive index of the material making up the core region of the compensating optical fibre length; b) the holes of the first and the at least one second ring are substantially of the same diameter d; and c) the ratio d/Λ substantially satisfies the following relationship (A) 0.8≦d/Λ&lt;1.

[0001] The present invention relates to a device for the compensation ofchromatic dispersion comprising a compensating optical fibre with a coreregion surrounded by a cladding region in which a plurality of holes ispresent which run along the compensating optical fibre longitudinally.

[0002] Furthermore, the present invention also relates to an opticalcommunication line comprising a transmission optical fibre lengthhaving, at a wavelength λ, a positive chromatic dispersion slope s_(t)and/or a positive chromatic dispersion coefficient D_(t) and acompensating optical fibre length with a negative chromatic dispersionslope s_(c) and/or a negative chromatic dispersion coefficient D_(c).

[0003] Furthermore, the present invention also relates to an opticalcommunication system comprising such an optical communication line and amethod for designing a compensating optical fibre so that, at apredefined wavelength λ, it has a negative chromatic dispersion slopes_(c) and/or a negative chromatic dispersion coefficient D_(c).

[0004] Throughout the present description and claims, the expression

[0005] “chromatic dispersion coefficient D” is used to indicate thefirst order dependency of the group velocity from the wavelength. Inparticular, the chromatic dispersion coefficient D is expressed asfollows (Govind P. Agrawal, “Nonlinear Fiber Optics—Second Edition”,Academic Press, pages 8-10)$D = {\frac{\beta_{1}}{\lambda} = {{- \frac{2\pi \quad c}{\lambda^{2}}}\beta_{2}}}$

[0006] where β₁, and β₂ are the constant of propagation of the mode ofthe first and, respectively, of the second order and D is expressed inps/(nm*Km);

[0007] “slope of chromatic dispersion s” is used to indicate thederivative, with respect to the wavelength, of the chromatic dispersioncoefficient D and is expressed in ps/(nm²*Km); and

[0008] “transmission optical fibre” is used to indicate an optical fibreused in a line or in an optical communication system for thetransmission of optical signals from one point to another one located ata significant distance.

[0009] As known, the optical fibres are commonly used in the field ofoptical telecommunications for the transmission of signals. Essentiallythey comprise an inner cylindrical region, called core, within which asignal is transmitted and an outer annular region, called cladding. Thecladding has a refractive index lower than that of the core in order toconfine the signal transmitted within the latter.

[0010] Typically, the core and the cladding are made from a silica basedvitreous material and the difference in the refractive index between thecore and the cladding is obtained by incorporating suitable additives(dopants) in the vitreous matrix of the core and/or of the cladding.

[0011] In the field of optical telecommunications and the propagation ofan optical signal in an optical fibre, the chromatic dispersion (orsecond order dispersion), defined by the above-mentioned coefficient D,is a phenomenon for which different spectral components of a pulse oflight that propagates in an optical fibre travel at different speedscausing a time spreading of the pulse.

[0012] In an optical communication system, the chromatic dispersionlimits, therefore, the maximum data transmission speed (that is, the bitrate) or the maximum length of a link without electrical regeneration ofthe signal.

[0013] Furthermore, chromatic dispersion is a phenomenon that depends onthe wavelength so that pulses of light at different wavelength propagatein an optical fibre at different speeds.

[0014] This last phenomenon, known as dispersion of the third order orchromatic dispersion slope (or “slope”) is a problem in wavelengthdivision multiplexing (WDM) optical communication system in which theinformation is transported along the same optical fibre by a pluralityof optical signals at different wavelengths.

[0015] In the WDM optical communication systems, therefore, it isnecessary to compensate not only the chromatic dispersion but also thechromatic dispersion slope in the range of wavelengths of interest.

[0016] Devices to compensate the chromatic dispersion as well as thechromatic dispersion slope of a conventional single mode fibre (SMF) areknown.

[0017] For example, devices are already known that comprise an opticalfibre suitably designed to have values of the chromatic dispersioncoefficient D and of the chromatic dispersion slope that are very highand of an opposite sign with regards to those of the SMF optical fibrefor which dispersion compensation is required.

[0018] Since the SMF optical fibres have a chromatic dispersioncoefficient D and a chromatic dispersion slope s that are positive, thedevices to compensate the dispersion, typically, have negative chromaticdispersion coefficient and chromatic dispersion slope.

[0019] T. Kashiwada et al. (“Broadband dispersion compensating moduleconsidering its attenuation spectrum behaviour for WDM system”, OFC '99,WM12, pages 229-231) describe an optical fibre, to compensate thedispersion of a SMF optical fibre with a W refractive index profiledesigned in order to obtain negative values of the chromatic dispersioncoefficient D and of the chromatic dispersion slope so as to compensatethe positive values of the SMF fibre.

[0020] G. E. Berkey et al. (“Negative slope dispersion compensatingfibers”, OFC '99, WM14, pages 235-237) describe an optical fibre, tocompensate the dispersion of a SMF optical fibre, with a refractiveindex profile designed in order to obtain negative values of thechromatic dispersion coefficient D and of the chromatic dispersion slopes in order to compensate the positive values of the SMF fibre.

[0021] L. Gruner-Nielsen et al. (“Design and manufacture of dispersioncompensating fibre for simultaneous compensation of dispersion anddispersion slope”, OFC '99, Technical Digest WM13, pages 232-234),describe an optical fibre, to compensate the dispersion of a SMF opticalfibre, with a depressed cladding and designed to obtain negative valuesof the chromatic dispersion coefficient D and of the chromaticdispersion slope s in order to compensate the positive values of the SMFfibre.

[0022] Furthermore, in the last few years the dispersion properties of aholey optical fibre have been studied.

[0023] A holey optical fibre is an optical fibre typically made of asingle type of material in which the difference in the refractive indexbetween the core and the cladding, which provides a guided propagation,is achieved through the presence of holes in the cladding which reducethe refractive index of the material from which the fibre is made.

[0024] In particular, a holey optical fibre has a cladding regioncomprising holes that run along the entire length of the fibre and acore region determined by the absence of at least one hole in thematerial.

[0025] The U.S. Pat. No. 5,802,236 patent describes a micro-structuredoptical fibre which includes a solid silica core region surrounded by ainner cladding region and an outer cladding region. The cladding regionhas capillary holes that extend in the axial direction of the fibre. Theholes in the outer cladding region are of a smaller diameter than theholes in the inner cladding region and therefore the effectiverefractive index of the outer cladding region is greater than theeffective refractive index of the inner cladding region. This documentstates that this type of fibre may have high negative values of thechromatic dispersion coefficient D (for example, values that are morenegative than −300 ps/nm*Km) at a predetermined wavelength (for example,1550 nm) and high negative values of the chromatic dispersion slope s sothat the fibre can carry out a dispersion compensation in a range ofwavelengths of 20 nm or more. Furthermore, a micro-structured opticalfibre is described in which the holes of the outer cladding region areof a diameter equal to 0.688 μm, the holes of the inner cladding regionhave a diameter equal to 0.833 μm and the centre to centre distance Λbetween the holes is 0.925 μm.

[0026] D. Mogilevtsev et al. (“Group velocity dispersion in photoniccrystal fibers”, Optics Letters, Vol. 23, No. 21, November 1998, pages1662-1664) study the properties of dispersion of photonic crystaloptical fibres and indicate that these fibres may have high values ofnormal (negative) chromatic dispersion coefficient D suitable tocompensate the chromatic dispersion at 1550 nm.

[0027] S. E. Barkou et al. (“Dispersion properties of photonic bandgapguiding fibers”, OFC '99, FG5, pages 117-119) investigate the dispersionproperties of a holey fibre. They point out that, by changing thedistance Λ between two centres of two adjacent holes from 1.4 μm to 2.9μm and in the range of wavelengths between 1.2 and 1.7 μm, very highpositive values of the chromatic dispersion coefficient can be achieved.Furthermore, for a value of Λ equal to 2.9 μm they point out that a veryflat dispersion curve can be achieved with a dispersion valueapproximately equal to zero at 1550 nm. Therefore, the Authors concludethat the holey optical fibres have dispersion characteristics verydifferent from the conventional ones, that may be designed for flat,non-zero dispersion over a wide wavelength range and that may exhibitdispersion significantly above the material dispersion.

[0028] T. M. Monro et al. (“Holey optical fibers: an efficient modalmodel”, Journal of Lightwave Technology, vol. 17, No. 6, June 1999,pages 1093-1102) describe a model for the propagation of light in holeyoptical fibres. With this model the Authors obtain a curve of thechromatic dispersion coefficient as a function of wavelength for Λ beingequal to 2.3 and values of the ratio d/Λ (where d is the diameter of theholes) equal to 0.1, 0.2 and 0.3. They indicate that as the hole size isincreased, the dispersion value induced by the holes increases (as whenthe holes are small the chromatic dispersion is dominated by thematerial dispersion).

[0029] T. A. Birks et al. (“Dispersion compensation usingsingle-material fibers”, IEEE Photonics Technology Letters, Vol. 11, No.6, June 1999, pages 674-676) propose a model for the propagation oflight in holey optical fibres according to which they approximate aholey fibre with holes of a large diameter with a fibre made up of asilica core in air. Through the use of this model, the authors calculatethat such fibres may have, at 1550 nm, a negative value of the chromaticdispersion coefficient of −2000 ps/(nm*Km) in order to compensate for aconventional optical fibre with a length 100 times greater. Furthermore,they calculate that such fibres may have, at 1550 nm, a chromaticdispersion slope of −2.3 ps*nm⁻²*Km⁻¹ with a negative chromaticdispersion value of −680 ps/(nm*Km) so that they may compensate aconventional optical fibre with a length 55 times greater over a 100 nmband centred around 1550 nm. Therefore, the Authors conclude that suchfibres have great potential for the compensation of chromaticdispersion.

[0030] T. M. Monro et al. (“Holey fibers with randomly arranged airholes”, CLEO 2000, San Francisco (USA), 7-12 May 2000, CFJ2 page 670)present a discussion aimed at illustrating that the light may be guidedin a holey optical fibre with air holes arranged randomly. They alsoindicate that in a holey fibre the d/Λ ratio determines a range ofpossible dispersion values and that when the holes are large they canobtain high coefficient values of chromatic dispersion that may benormal (negative) or anomalous (positive).

[0031] A holey optical fibre may be produced by forming a preformstarting from a bundle of empty tubes arranged according to apredetermined structure in which the central tube is replaced by a solidbar which will make up the core region of the fibre. The preformachieved in this way is then spinned in order to achieve a holey opticalfibre with holes of diameter d and pitch Λ. The spinning processgenerally allows for the initial structure of the arrangement of thetubes in the preform to remain almost unchanged and, therefore, toachieve the desired value of pitch Λ with a high level of precision.

[0032] However, with regards to the diameter d of the holes, theApplicant has noted that during the spinning process of the preform, thediameter of the tubes may vary so that it is not be possible to achievewith as much precision the desired value of the diameter d (and,therefore of the ratio d/Λ).

[0033] The Applicant, therefore, has noted that the ratio d/Λ is acritical parameter in the production process of an optical fibre.

[0034] The Applicant, therefore, has faced the technical problem ofproviding an optical communication line with a holey compensatingoptical fibre with negative dispersion features stable with respect tothe variations of the parameter d/Λ.

[0035] Therefore, in a first aspect the present invention relates to anoptical communication line comprising

[0036] a transmission optical fibre length with, at a wavelength λ, apositive chromatic dispersion slope s_(t);

[0037] a compensating optical fibre length, associated to saidtransmission optical fibre length, with a negative chromatic dispersionslope s_(c) suitable to compensate, at least partly, the positivechromatic dispersion slope s_(t) of the transmission fibre, saidcompensating optical fibre having a core region surrounded by a claddingregion, the cladding region defining a first ring of holes, whichsubstantially defines, around the core region, an annulus with an innerradius r1 and an outer radius r2, and at least one second ring of holesthat surrounds the first ring of holes, said holes running along thecompensating optical fibre longitudinally and being spaced apart fromeach other substantially according to a predefined pitch Λ,

[0038] in which

[0039] a) the values of said inner radius r1 and said outer radius r2are selected in such a way that the wavelength in the means, λ/n, isincluded in the range of values defined by r1 and r2, that is to say insuch a way that the following relationship (L) is substantiallysatisfied

r1≦λ/n≦r2

[0040]  wherein n is the refractive index of the material making up thecore region of said compensating optical fibre length

[0041] b) the holes of said first and said at least one second ring aresubstantially of the same diameter d, and

[0042] c) the ratio d/Λ substantially satisfies the followingrelationship (A)

0.8≦d/Λ<1.

[0043] The Applicant, in fact, has found that a compensating opticalfibre according to the invention, in which the first ring of holesdefines an annulus with radiuses r1 and r2 such that the wavelength λ/nis comprised between the values r1 and r2, has a negative chromaticdispersion slope s_(c) suitable to compensate at least in part thepositive chromatic dispersion slope s_(t) of the transmission fibre.

[0044] Furthermore, the Applicant has found that a compensating opticalfibre having, according to the invention, a negative chromaticdispersion slope s_(c), a first and at least one second ring of holes ofa diameter d substantially equal and a ratio d/Λ≧0.8, has stabledispersion features with respect to modification of the parameter d/Λ.That is, the dispersion features of such a compensating optical fibrevary slowly upon variation of the parameter d/Λ.

[0045] This advantageously allows to achieve a compensating opticalfibre with dispersion features that are not very sensitive tovariations, due to the production process, of the parameter d/Λ withrespect to the desired value.

[0046] Furthermore, a compensating optical fibre having, according tothe invention, a first and at least one second ring of holes with adiameter substantially equal advantageously allows to simplify theproduction process of the fibre.

[0047] Moreover, the Applicant noted that in a compensating opticalfibre according to the invention the diameter d of the holes that allowsto achieve dispersion features useful for practical applications inoptical communication lines and systems is relatively high.

[0048] Preferably, the value of d is comprised between approximately0.75 and 1.1 μm. More preferably, the value of d is comprised betweenapproximately 0.8 and 1.1 μm.

[0049] Relatively high values of the diameter d advantageously allow forthe semplification of the production process of the compensating fibre.Furthermore, they allow for the achievement of relative long lengths ofcompensating fibre (typically in the order of a few kilometres) withoutthe risk of collapse of the holes.

[0050] Advantageously, the value of Λ substantially satisfies thefollowing relationship (C)${\frac{\lambda}{n}*\frac{1}{1 + {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}} \leq \Lambda \leq {\frac{\lambda}{n}*\frac{1}{1 - {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}}$

[0051] The Applicant has in fact found that the above-mentionedrelationship (L) is satisfied when the pitch Λ substantially satisfiesthe above-mentioned relationship (C).

[0052] Preferably, the ratio d/Λ substantially satisfies the followingrelationship

0.9≦d/Λ<1.

[0053] The Applicant has in fact verified that the stability of thedispersion features of the compensating fibre increase for a value ofthe ratio d/Λ comprised between 0.9 and 1.

[0054] Furthermore, for a value of the ratio d/Λ comprised between 0.9and 1, the Applicant has verified that the compensation efficiency ofthe compensating optical fibre length typically increases.

[0055] Advantageously, said wavelength λ is comprised betweenapproximately 1300 nm and 1700 nm. Preferably, it is comprised between1450 and 1600 nm. More preferably, it is comprised within the thirdtransmission band of the optical fibres (that is between 1500 and 1600nm). Even more preferably, it is comprised within the typicaltransmission band of an optical amplifier doped with erbium (that isbetween 1530 and 1600 nm).

[0056] The compensating optical fibre length is placed within, upstreamor, advantageously, downstream said transmission optical fibre length.

[0057] Typically,

[0058] the transmission optical fibre length has a length L_(t);

[0059] the compensating optical fibre length has a length L_(c); and

[0060] the value of said length L_(c) and of said chromatic dispersionslope s_(c) of said compensating optical fibre length are such that theproduct s_(c)*L_(c) is substantially equal to the product −s_(t)*L_(t)in order to compensate the chromatic dispersion slope of thetransmission optical fibre length.

[0061] This allows to achieve an optical communication line with achromatic dispersion substantially constant with respect to wavelengthand is particularly advantageous in the case of a WDM opticalcommunication line suitable to transmit a plurality of signals havingdifferent wavelengths.

[0062] Preferably, the value of Λ satisfies the following relationship(D)${\Lambda ({\mu m})} = {0.4 + {\frac{0.44}{d/\Lambda} \pm {0.02\quad {\mu m}}}}$

[0063] in order to achieve a negative value of the chromatic dispersionslope s_(c) suitable to efficiently compensate the chromatic dispersionslope of said transmission optical fibre length.

[0064] The Applicant has found that the above-mentioned relationship Dallows to achieve, within the values of Λ contemplated by theabove-mentioned relationship C, an optimal value of Λ corresponding to ahigh absolute value of the chromatic dispersion slope s_(c). This,advantageously, allows to compensate the dispersion s_(t)*L_(t) of thetransmission optical fibre length with a short length L_(c) of thecompensating optical fibre length.

[0065] Typically, in said optical communication line

[0066] the transmission optical fibre length also has, at the wavelengthλ, a positive chromatic dispersion coefficient D_(t); and

[0067] the value of Λ substantially satisfies, advantageously, thefollowing relationship (F)${{\Lambda ({\mu m})} = {{\alpha*\frac{D_{t}}{s_{t}}} + {\beta \pm {0.02\quad {\mu m}}}}},{where}$${\alpha = {{{- 10^{- 4}}*\left( {{2.685*\frac{d}{\Lambda}} + 5.987} \right)\quad {and}\quad \beta} = {{{- 3.4}\left( {\frac{d}{\Lambda} - 1} \right)^{3}} + 1.18}}}\quad$

[0068] The Applicant has in fact found that the above-mentionedrelationship (F) makes sure that the compensating optical fibre lengthhas such a chromatic dispersion coefficient D_(c) and such a chromaticdispersion slope s_(c) that the ratio D_(c)/s_(c) is substantially equalto the ratio D_(t)/s_(t). Advantageously, this allows to compensate thechromatic dispersion slope as well as the chromatic dispersion of thetransmission optical fibre length.

[0069] Typically, said optical communication line also comprises anoptical amplifier.

[0070] Preferably, said optical amplifier is placed downstream saidcompensating optical fibre length.

[0071] Advantageously, said amplifier is of the type provided with anactive optical fibre doped with a rare earth.

[0072] Typically, said rare earth is erbium.

[0073] Typically, said core region of the compensating optical fibrelength is made from a silica based vitreous material.

[0074] Typically, also said cladding region of the compensating opticalfibre is made from a silica based vitreous material.

[0075] However, the core and the cladding regions are not necessarilymade from the same material.

[0076] Typically the holes defined by the cladding region are filledwith air. Alternatively, they are filled with another material with arefractive index below that of the material that makes up the coreregion. For example, such material is a gas. In particular, a gas thatdoes not interact chemically with the material of the core and claddingregions.

[0077] Advantageously, said cladding region also defines at least onethird ring of holes placed around said at least one second ring ofholes.

[0078] Said rings of holes can be of any shape whatsoever. Typically,they are of a hexagonal shape. In general, they have a circularsymmetry.

[0079] Typically, said transmission optical fibre length is aconventional optical fibre essentially consisting of a core and acladding with a refractive index lower than that of the core in order toconfine the signal transmitted within the latter.

[0080] Typically, the core and the cladding are made from a silica basedvitreous material and the difference in the refractive index between thecore and the cladding is obtained by incorporating suitable dopants(such as, for example, germanium, phosphorus and/or fluorine) in thevitreous matrix of the core and/or the cladding.

[0081] Typically said transmission optical fibre length is aconventional single mode optical fibre (SMF) produced, for example, byFOS or CORNING Inc.

[0082] Advantageously, said transmission optical fibre length isselected from the group comprising a True Wave™ (TF) optical fibre, aTrue Wave Plus™ (TW+) optical fibre, a True Wave RS™ (TW RS) opticalfibre produced by LUCENT Technology Inc.; a large effective area opticalfibre (or LEAF), a LEAF Enhanced optical fibre produced by CORNING Inc.and a Freelight™ optical fibre produced by FOS.

[0083] In a second aspect the present invention also relates to anoptical communication system comprising

[0084] a transmitting station suitable to supply an optical signal witha wavelength signal λ;

[0085] a receiving station suitable to receive said optical signal;

[0086] an optical communication line, optically connected to saidtransmitting station and said receiving station, to transmit saidoptical signal, said line including at least one transmission opticalfibre length, having at a wavelength λ a positive chromatic dispersionslope s_(t), and a compensating optical fibre length, associated to saidtransmission optical fibre length, with a negative chromatic dispersionslope s_(c) suitable to compensate at least in part the positivechromatic dispersion slope s_(t) of the transmission fibre, saidcompensating optical fibre having a core region surrounded by a claddingregion, the cladding region defining a first ring of holes, whichsubstantially defines, around the core region, an annulus with an innerradius r1 and an outer radius r2 and at least one second ring of holesthat surrounds the first ring of holes, said holes running along thecompensating optical fibre longitudinally and being spaced apart fromeach other substantially according to a predefined pitch Λ,

[0087] in which

[0088] a) the values of said inner radius r1 and said outer radius r2are selected in such a way as to satisfy the following relationship (L)

r1≦λ/n≦r2

[0089]  wherein n is the refractive index of the material making up thecore region of said compensating optical fibre length,

[0090] b)the holes of the said first and said at least one second ringare substantially of the same diameter d, and

[0091] c)the ratio d/Λ substantially satisfies the followingrelationship (A)

0.8≦d/Λ<1.

[0092] Advantageously, said optical signal is a WDM optical signalcomprising a plurality of N signals having wavelengths λ1, λ2 . . . λN.

[0093] With regards to the structural and functional features of saidoptical communication line, of said fibre transmission length and ofsaid compensating optical fibre length reference shall be made to whatalready described above.

[0094] In a third aspect thereof the present invention also relates to amethod for the design of a compensating optical fibre so that it has, ata predefined wavelength λ, a negative chromatic dispersion slope s_(c),said compensating optical fibre having a core region surrounded by acladding region, the cladding region defining a first ring of holes,that substantially defines, around the core region, an annulus with aninner radius r1 and an outer radius r2, said holes running along thecompensating optical fibre longitudinally, having a diameter d and beingsubstantially spaced apart from each other according to a predefinedpitch Λ, said method including the steps of

[0095] a) selecting a value of the ratio d/Λ through the followingrelationship (B)

0.5≦d/Λ<1, and

[0096] b) selecting the values of said inner radius r1 and said outerradius r2 in such a way that the following relationship (L) issubstantially satisfied

r1≦λ/n≦r2

[0097]  wherein n is the refractive index of the material making up thecore region of said compensating optical fibre.

[0098] Advantageously, step b) is carried out by selecting the value ofΛ by means of the following relationship (C)${\frac{\lambda}{n}*\frac{1}{1 + {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}} \leq \Lambda \leq {\frac{\lambda}{n}*\frac{1}{1 - {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}}$

[0099] and once the value of Λ has been selected, the value of d isdetermined by the value of the ratio d/Λ selected in step a).

[0100] Preferably, step b) is carried out by selecting the value of Λ bymeans of the following relationship (D)${\Lambda ({\mu m})} = {0.4 + {\frac{0.44}{d/\Lambda} \pm {0.02\quad {\mu m}}}}$

[0101] in such a way as to achieve an efficient compensating opticalfibre.

[0102] When it is required to design the compensating optical fibre sothat it has a negative chromatic dispersion coefficient D_(c) and sothat it is capable of compensating a positive chromatic dispersioncoefficient D_(t) and a positive chromatic dispersion slope S_(t), stepb) is carried out by selecting the value of Λ in order to satisfy thefollowing relationship (E)${\Lambda ({\mu m})} = {{\alpha*\frac{D_{t}}{s_{t}}} + {\beta \pm {0.02\quad {\mu m}\quad {where}}}}$$\alpha = {{- 10^{- 4}}*\left( {{2.685*\frac{d}{\Lambda}} + 5.987} \right)}$$\beta = {{{3.14*\left( \frac{d}{\Lambda} \right)^{2}} - {5.162*\frac{d}{\Lambda}} + {3.3476\quad {for}\quad 0.5}} \leq {d/\Lambda} < 0.7}$$\beta = {{{{- 3.4}\left( {\frac{d}{\Lambda} - 1} \right)^{3}} + {1.18\quad {for}\quad 0.7}} \leq {d/\Lambda} < 1}$

[0103] in such a way that the chromatic dispersion coefficient D_(c) andthe chromatic dispersion slope s_(c) of said compensating optical fibreare such that the ratio D_(c)/s_(c) is substantially equal to the ratioD_(t)/s_(t).

[0104] Preferably, the ratio d/Λ substantially satisfies the followingrelationship

0.7≦d/Λ<1.

[0105] More preferably, the ratio d/Λ substantially satisfies thefollowing relationship

0.8≦d/Λ<1.

[0106] Preferably, the value of d is comprised between approximately0.75 and 1.1 μm. More preferably, the value of d is comprised betweenapproximately 0.8 and 1.1 μm.

[0107] Advantageously, said wavelength λ is comprised betweenapproximately 1300 nm and 1700 nm. Preferably, it is comprised between1450 and 1600 nm. More preferably, it is comprised in the thirdtransmission band of the optical fibres (that is between 1500 and 1600nm). Even more preferably, it is comprised in the typical transmissionband of an optical amplifier doped with erbium (that is between 1530 and1600 nm).

[0108] In a fourth aspect thereof the present invention also relates toa method for determining the parameters d and Λ of a compensatingoptical fibre so that it has, at a predefined wavelength λ, a negativechromatic dispersion coefficient D_(c), said compensating optical fibrehaving a core region surrounded by a cladding region, the claddingregion defining a first ring of holes around the core region, said holesrunning along the compensating optical fibre longitudinally, having adiameter d and being spaced apart from each other substantiallyaccording to a predefined pitch Λ, said method including the steps of

[0109] a) selecting a value of the ratio d/Λ through the followingrelationship (G)

0.5≦d/Λ<1,

[0110] b) selecting a value of Λ through the following relationship (H)$\Lambda = {{\frac{\lambda}{n}\left( \frac{1}{1 + {\frac{1}{2}\frac{d}{\Lambda}}} \right)} \pm {0.25\quad {\mu m}}}$

[0111]  wherein n is the refractive index of the material making up thecore region of said compensating optical fibre and

[0112] c) once the value of Λ has been selected, determining the valueof d through the value of the ratio d/Λ selected in step a).

[0113] With regards to the ratio d/Λ, the diameter d and the wavelengthλ, reference shall be made to what described above.

[0114] In a fifth aspect thereof the present invention also relates to adevice for the compensation of the chromatic dispersion and/or thechromatic dispersion slope comprising a compensating optical fibrelength comprising, in turn, a core region surrounded by a claddingregion, the core region defining a first ring of holes, whichsubstantially defines, around the core region, an annulus with an innerradius r1 and an outer radius r2, and at least one second ring of holesthat surrounds the first ring of holes, said holes running along thecompensating optical fibre longitudinally and being spaced apart fromeach other substantially according to a predefined pitch Λ,

[0115] in which

[0116] a) the values of said inner radius r1 and said outer radius r2are such that they satisfy the following relationship (L)

r1≦λ/n≦r2

[0117]  wherein n is the refractive index of the material that makes upthe core region of said compensating optical fibre length

[0118] b) the holes of said first and said at least one second ring aresubstantially of the same diameter d, and

[0119] c) the ratio d/Λ substantially satisfies the followingrelationship (A)

0.8≦d/Λ<1.

[0120] With regards to the features of said compensating optical fibrereference shall be made to what described above with regards to thecompensating optical fibre length of the optical communication line ofthe invention.

[0121] In a further aspect thereof, the present invention also relatesto a device for the compensation of the chromatic dispersion and/or thechromatic dispersion slope comprising a compensating optical fibrecomprising, in turn, a core region surrounded by a cladding region, thecladding region defining a first ring of holes that surrounds the coreregion and at least one second ring of holes that surrounds the firstring of holes, said holes running along the compensating optical fibrelongitudinally and being spaced apart from each other substantiallyaccording to a predefined pitch Λ, in which

[0122] the holes of said first and said at least second ring aresubstantially of the same diameter d,

[0123] the ratio d/Λ substantially satisfies the following relationship(A)

0.8≦d/Λ<1, and

[0124] the value of Λ is comprised between approximately 0.95 and 1.21μm.

[0125] Advantageously, the value of Λ is comprised between approximately0.95 and 1.18 μm.

[0126] Advantageously, for a ratio d/Λ equal to approximately 0.8, thevalue of Λ is comprised between approximately 1 and 1.21 μm. Preferably,for a ratio d/Λ equal to approximately 0.8, it is comprised betweenapproximately 1 and 1.18 μm.

[0127] Advantageously, for a ratio d/Λ comprised between approximately0.9 and 1, the value of Λ is comprised between approximately 0.96 and1.18 μm. Preferably, for a ratio d/Λ comprised between approximately 0.9and 1, it is comprised between approximately 0.96 and 1.16 μm.

[0128] With regards to the features of said compensating optical fibrereference shall be made to what described above relating to thecompensating optical fibre length of the optical communication line ofthe invention.

[0129] Further features and advantages of the present invention willbecome clear from the following detailed description of a preferredembodiment, made with reference to the drawings attached. In suchdrawings,

[0130]FIG. 1 illustrates a first embodiment of an optical communicationline according to the invention;

[0131]FIG. 2 illustrates a second embodiment of an optical communicationline according to the invention;

[0132]FIG. 3 illustrates an optical communication system according tothe invention;

[0133]FIG. 4 illustrates a schematic representation of an embodiment ofa compensating optical fibre length according to the invention;

[0134]FIG. 5 illustrates the pattern of the chromatic dispersioncoefficient D_(c) of a compensating optical fibre length of the line ofFIG. 1 with respect to the wavelength λ and the value of the parameter Λfor a ratio d/Λ equal to 0.8;

[0135]FIG. 6 illustrates an optical amplifier of the line and of thesystem of FIGS. 2 and 3;

[0136]FIG. 7 illustrates the pattern of the parameter Λ with respect tothe ratio D/s, for different values of d/Λ greater or equal to 0.5,achieved by resolving the Maxwell equations (full line) and according tothe method of the invention (dotted line);

[0137]FIG. 8 illustrates the propagation delay (calculated with respectto the propagation time at 1550 nm) with respect to the wavelength λalong an optical communication line comprising 100 Km of transmissionoptical fibre of the SMF type and 6.4 Km of compensating optical fibreaccording to the invention for d/Λ=0.8;

[0138]FIG. 9 illustrates the residual dispersion coefficient D of anoptical communication line comprising 100 Km of optical fibretransmission of the SMF type and 6.4 Km of compensating optical fibreaccording to the invention for d/Λ=0.8;

[0139]FIG. 10 illustrates the pattern of the ratio D/s with respect tothe ratio d/Λ for values of Λ equal to 1, 1.1 and 1.15 μm of acompensating optical fibre designed according to the invention.

[0140]FIG. 1 shows an optical communication line 1 according to theinvention comprising a transmission optical fibre length 10 and acompensating optical fibre length 12, placed downstream the length 10.

[0141] The transmission optical fibre length 10 is a length of opticalfibre conventionally used for telecommunications.

[0142] More in particular, it is a length of optical fibre comprising acore and a cladding, both of which are made from a silica based vitreousmaterial, in which the difference in the refractive index between thecore and the cladding is achieved by incorporating suitable dopants inthe vitreous matrix and/or the cladding.

[0143] Typical examples of such kinds of optical fibres are, as alreadymentioned above, a SMF conventional optical fibre, a True Wave™ opticalfibre, a True Wave Plus™ optical fibre, a True Wave RS™ optical fibre, aLEAF optical fibre, a LEAF Enhanced optical fibre and a FreeLight™optical fibre.

[0144] At a wavelength λ, the transmission optical fibre length 10 has apositive chromatic dispersion slope s_(t).

[0145] Furthermore, it is of a length L_(t) that can range from a fewkilometres to a few hundred kilometres. Typically, its length L_(t) isbetween 30-200 Km.

[0146] The compensating optical fibre length 12 is a length of holeyoptical fibre having a core region 13 and a cladding region 14 thatsurrounds the core region 13 (FIG. 4).

[0147] The cladding region 14 comprises, for example, two rings of holesthat surround that core region 13.

[0148] In the embodiment illustrated in FIG. 4, the two rings of holesare of a hexagonal shape.

[0149] The holes run along the compensating optical fibre length 12lengthwise for the entire length.

[0150] Furthermore, in the embodiment illustrated, the core region 13and the cladding region 14 are both made up of a silica based vitreousmaterial and the holes are filled with air.

[0151] The holes of the two rings are of a substantially equal diameterand are spaced apart from each other by a pitch Λ.

[0152] The compensating optical fibre length 12 can be producedaccording to a known method such as, for example, the one described bythe U.S. Pat. No. 5,802,236.

[0153] According to the method of the invention, the compensatingoptical fibre length 12 can be designed in such a way as to have, at thewavelength λ, a negative chromatic dispersion slope s_(c) and compensateat least in part the positive chromatic dispersion slope s_(t) of thetransmission optical fibre length 10.

[0154] More in particular, in order that the compensating optical fibrelength 12 has, at the wavelength λ, a negative chromatic dispersionslope s_(t), it must be designed in such a way that the parameters d andΛ substantially satisfy the above mentioned relations B and C:

−0.5≦d/Λ<1   (B) $\begin{matrix}{{\frac{\lambda}{n}*\frac{1}{1 + {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}} \leq \Lambda \leq {\frac{\lambda}{n}*\frac{1}{1 - {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}}} & (C)\end{matrix}$

[0155] where λ is the wavelength in the vacuum, n is the refractiveindex of the material that makes up the core region 13 (and the claddingregion 14 when it is made up of the same material of the core region 13)of the compensating optical fibre length 12 and λ/n is the wavelength inthe propagation means.

[0156] The Applicant has verified that the relationship C is in fullagreement with the corresponding values of Λ that are achieved byresolving the Maxwell equations in an range of wavelengths comprisedbetween 1300 and 1700 nm.

[0157] More in particular, the relationship C provides an excellentapproximation of the values of Λ (with a margin of error in the order ofa few nm) around the wavelength of 1550 nm, for a material with arefractive index n approximately equal to that of the silica(approximately 1.45) and for a value of d/Λ of at least approximately0.7.

[0158] The compensating optical fibre 12 designed in this way has anegative chromatic dispersion slope s_(t) suitable to compensate, atleast in part, the positive chromatic dispersion slope of thetransmission optical fibre length 10.

[0159] For example, considering

[0160] a wavelength λ of 1550 nm,

[0161] a ratio d/Λ equal to 0.8,

[0162] a refractive index n equal to 1.45 (approximately equal to therefractive index of the silica at 1550 nm), the compensating opticalfibre 12 designed according to the method of the invention has anegative chromatic dispersion slope s_(c) for a value of Λ includedbetween approximately 0.76 μm and approximately 1.78 μm.

[0163] Once the value of Λ has been selected within such interval, thevalue of d is determined by the relationship d/Λ=0.8.

[0164]FIG. 5 illustrates the pattern of the chromatic dispersioncoefficient D_(c) (expressed in ps/(nm*Km)) of the compensating opticalfibre length 12 with respect to the wavelength λ and the value of theparameter Λ for d/Λ=0.8.

[0165] Such a pattern has been determined by resolving the vectorialMaxwell equations of the propagation of light in a holey optical fibreas described, for example, by Ferrando et al. (“Full-vector analysis ofrealistic photonic crystal fiber”, Optics Letters, Vol. 24, No. 5, March1999, pages 276-278) and by Silvestre et al. (“Biothermal basis methodfor the vector description of optical fiber modes”, Journal of LightwaveTechnology, Vol. 16, No. 5, pages 923-928).

[0166] From the pattern of the chromatic dispersion coefficient D_(c) ofFIG. 5 an excellent correspondence between the values of Λ foundaccording to the invention in conformity with the above-mentionedrelationship C, to achieve a negative chromatic dispersion slope at awavelength of 1550 nm, and those found by resolving the Maxwellequations can be noted.

[0167] Furthermore, according to the method of the invention it is alsopossible to determine the value of Λ which, within the range of valuesfound with the relations B and C, allows for the optimisation of thevalue of the chromatic dispersion slope s_(c) of the compensatingoptical fibre length 12. In other words, the value of Λ which allows forthe achievement of a high absolute value of s_(c) in order to compensatethe dispersion s_(t)*L_(t) of the transmission optical fibre length 10with a very short length L_(c) of the compensating optical fibre length12.

[0168] More in particular, in order to optimise the value of thenegative chromatic dispersion slope s_(t), the compensating opticalfibre length 12 must be designed, according to the method of theinvention, in such a way that the parameter Λ satisfies, as well as theabove-mentioned relations B and C, also the relationship (D):${\Lambda ({\mu m})} = {0.4 + {\frac{0.44}{d/\Lambda} \pm {0.02\quad {\mu m}}}}$

[0169] The Applicant has verified that the relationship D is in fullagreement with the corresponding values of Λ that are achieved byresolving the Maxwell equations in a range of wavelengths between 1300and 1700 nm.

[0170] More in particular, the relation${\Lambda ({\mu m})} = {0.4 + \frac{0.44}{d/\Lambda}}$

[0171] provides an excellent approximation of the values of Λ (with amargin of error in the order of a few nm) around the wavelength of 1550nm, for a material with a refractive index n approximately equal to thatof the silica (approximately 1.45) and for a value of d/Λ of at least0.7.

[0172] For example, considering a ratio d/Λ equal to 0.8, the value of Λwhich allows to optimise the negative chromatic dispersion slope s_(c)of the compensating optical fibre length 12 is equal, according to therelations B-D of the method of the invention, to approximately 0.95 μm.According to the relationship d/Λ=0.8, this value of Λ corresponds to avalue of d equal to approximately 0.76 μm.

[0173] For a value of d equal to 0.76 μm, Λ equal to 0.95 μm, λ equal to1550 nm and n equal to 1.45, we find that the compensating optical fibrelength 12 has a chromatic dispersion slope s_(c) equal to −1.0869ps/(nm²*Km).

[0174] With this value of the chromatic dispersion slope s_(c), in orderto compensate the chromatic dispersion slope s_(t) of the transmissionoptical fibre length 10 having length L_(t), it is advantageous that thecompensating optical fibre length 12 has a length L_(c) equal toapproximately (L_(t)*s_(t))/s_(c).

[0175] For example, in the case that the transmission optical fibrelength 10 is a SMF fibre with a length L_(t) equal to 100 Km's and achromatic dispersion slope s_(t) equal to 0.0677 ps/(nm²*Km), the lengthL_(c) of the compensating optical fibre length 12 must be equal,according to the invention, to approximately 6.22 Km's.

[0176] Table 1 illustrates the typical values of D_(t), s_(t) andD_(t)/s_(t) of the conventional SMF, TW™, TW+™, TW RS™, LEAF, LEAFEnhanced, Freelight™ optical fibres. TABLE 1 D_(t) @ 1550 nm s_(t) @1550 nm D_(t)/s_(t) @ 1550 nm Type of fibre ps/(nm*km) ps/(nm²*km) (nm)SMF 17.0 0.0677 251.1 TW ™ 2.4 0.0715 33.5 TW + ™ 4 0.0715 55.9 TW RS ™5.7 0.045 126.6 LEAF 3.7 0.105 35.2 LEAF Enh. 4.3 0.09 47.7 FreeLight ™4.2 0.08 52.5

[0177] Table 2 illustrates the optimal values of Λ, d and L_(c) achievedby the relations B-D of the method of the invention for a value of d/Λequal to 0.8 to compensate in an efficient way the positive chromaticdispersion slope s_(t) of the transmission optical fibre length 10 inthe case that the length L_(t) is equal to 100 Km and in the differentcases in which it is made up of a SMF, TW™, TW+™, TW RS™, LEAF, LEAFEnhanced and Freelight™ optical fibre.

[0178] Furthermore, table 2 illustrates the values of s_(c) achieved at1550 nm, for a refractive index n equal to 1.45, in correspondence tothe values of d and Λ of Table 2. TABLE 2 Type of Λ d L_(c) s_(c) fibre(μm) (μm) (Km) ps/(nm²*km) SMF 0.95 0.76 6.23 −1.0869 TW ™ 0.95 0.766.58 −1.0869 TW + ™ 0.95 0.76 6.58 −1.0869 TW RS ™ 0.95 0.76 4.14−1.0869 LEAF 0.95 0.76 9.66 −1.0869 LEAF Enh. 0.95 0.76 8.28 −1.0869FreeLight ™ 0.95 0.76 7.36 −1.0869

[0179] The optical communication line 1 according to the invention can,therefore, compensate the chromatic dispersion slope not only of aconventional single mode optical fibre (SMF) but also of othertransmission optical fibres such as, for example, those listed in table2.

[0180] The optical communication lines 1 according to the invention can,therefore, have the chromatic dispersion slope s_(t) of the transmissionoptical fibre length compensated in an efficient way.

[0181] Such lines can, for example, be used in a WDM opticalcommunication system within which a constant chromatic dispersion isrequired with respect to the wavelength of the signals (that is analmost null chromatic dispersion slope).

[0182] In the case that a positive chromatic dispersion coefficientD_(t) of the transmission optical fibre length 10 is also to becompensated, the communication line 1 also comprises a conventionaldevice for the compensation of the chromatic dispersion made up of, forexample, a conventional optical circulator associated to a suitablechirped optical fibre Bragg grating or a conventional optical fibre tocompensate the chromatic dispersion.

[0183] Alternatively, in order to compensate also the chromaticdispersion of the transmission optical fibre length 10, the compensatingoptical fibre length 12 can be designed, according to the method of theinvention, to compensate both the chromatic dispersion and the chromaticdispersion slope of the transmission optical fibre length 10.

[0184] It is known that in order to compensate both the chromaticdispersion coefficient D_(t) and the chromatic dispersion slope s_(t) itis necessary to satisfy both of the following relationships

D _(t) *L _(t) +D _(c) *L _(c)=0

s _(t) *L _(t) +s _(c) *L _(c)=0

[0185] that is, it is necessary that the D_(t)/s_(t) ratio is equal tothe D_(c)/s_(c) ratio.

[0186] According to the invention, to compensate a positive chromaticdispersion coefficient D_(t) and a positive chromatic dispersion slopes_(t) of the transmission optical fibre length 10, the compensatingoptical fibre length 12 must be designed in such a way that theparameters d and Λ satisfy, besides the relations B and C, also thefollowing relationship (E):${\Lambda ({\mu m})} = {{\alpha*\frac{D_{t}}{s_{t}}} + {\beta \pm {0.02\quad {\mu m}\quad {where}}}}$$\alpha = {{- 10^{- 4}}*\left( {{2.685*\frac{d}{\Lambda}} + 5.987} \right)}$$\beta = {{{3.14*\left( \frac{d}{\Lambda} \right)^{2}} - {5.162*\frac{d}{\Lambda}} + {3.3476\quad {for}\quad 0.5}} \leq {d/\Lambda} < 0.7}$$\beta = {{{{- 3.4}\left( {\frac{d}{\Lambda} - 1} \right)^{3}} + {1.18\quad {for}\quad 0.7}} \leq {d/\Lambda} < 1}$

[0187] The Applicant has verified that the relationship E is in fullagreement with the corresponding values of Λ that are achieved byresolving the Maxwell equations in a range of wavelength comprisedbetween 1300 and 1700 nm.

[0188] More in particular, the relation${\Lambda ({\mu m})} = {{\alpha*\frac{D_{t}}{s_{t}}} + \beta}$

[0189] provides an excellent approximation of the values of Λ (with amargin of error in the order of a few nm's) around the wavelength of1550 nm and for a material with a refractive index n equal toapproximately that of the silica at 1550 nm (approximately 1.45).

[0190] For example, FIG. 7 illustrates the pattern of Λ with respect tothe ratio D/s, at different value of d/Λ, achieved through therelationship E of the method of the invention (dotted lines) andresolving the Maxwell equations (full lines) for a wavelength of 1550 nmand a refractive index n equal to that of the silica at 1550 nm(approximately 1.45).

[0191] The results achieved show an excellent correspondence between thevalues of Λ achieved according to the invention and resolving theMaxwell equations.

[0192] Furthermore, the results of FIG. 7 show how, for a compensatingoptical fibre 12 according to the invention, with a value of the ratiod/Λ greater or equal to 0.8, the variation in the ratio D/s issignificantly stable with respect to the ratio d/Λ compared with thecase of a ratio d/Λ lower than 0.8. Furthermore, such stabilityincreases significantly for a ratio d/Λ equal to least 0.9.

[0193] The stability of the ratio D/s with respect to the ratio d/Λ, fora value of the ratio d/Λ greater or equal to 0.8, is, furthermore, clearfrom FIG. 10 that illustrates the pattern of the ratio D/s (expressed innm) with respect to the ratio d/Λ for a value of Λ equal to 1, 1.1 and1.15 μm.

[0194] Furthermore, the Applicant has verified that the maximumvariation of the ratio D/s for a compensating optical fibre according tothe invention is only of approximately −520 nm for a variation in theratio d/Λ from 0 to 1. That is, a maximum variation in the ratio D/s ofonly approximately −5.2 nm corresponds to a variation of 0.01 in theratio d/Λ.

[0195] Furthermore, the Applicant has verified that a variation of 0.01in the ratio d/Λ, around a value of d/Λ of 0.9, corresponds to avariation in the ratio D/s of only approximately —1.4 nm, while avariation of 0.01 of the ratio d/Λ, around a value of d/Λ of 0.95,corresponds to a variation of the ratio D/s only of approximately −0.75nm.

[0196] Table 3 illustrates the values of Λ, d, L_(c) achieved with therelations B, C and E of the method of the invention for a value of d/Λequal to 0.8 to compensate both the chromatic dispersion slope s_(t) andthe chromatic dispersion coefficient D_(t) of the transmission opticalfibre length 10, in the case of length L_(t) equal to 100 Km and in thedifferent cases in which it is made up of a SMF, TW™, TW+™, TW RS™,LEAF, LEAF Enhanced and FreeLight™ optical fibre (the typical values ofD_(t), s_(t) and D_(t)/s_(t) of these optical fibres are illustrated inTable 1).

[0197] Furthermore, Table 3 illustrates the values of the ratioD_(c)/s_(c) and of D_(c) achieved at 1550 nm, for a refractive index nequal to 1.45 and in correspondence to the values of d and Λ of Table 3.TABLE 3 Type of Λ d L_(c) D_(c)/s_(c) D_(c) fibre (μm) (μM) (Km) (nm)ps/(nm*Km) SMF 1 0.8 6.4 257.45 −266.81 TW ™ 1.18 0.94 8.8 43.008−27.218 TW+ ™ 1.16 0.92 7.8 74.369 −51.298 TW RS ™ 1.1 0.88 5.2 133.87−108.59 LEAF 1.18 0.94 13.6 43.008 −27.218 LEAF Enh. 1.16 0.93 11 58.875−38.911 FreeLight ™ 1.16 0.93 10.8 58.875 −38.911

[0198] The optical communication line 1 according to the invention can,therefore, compensate both the chromatic dispersion slope and thechromatic dispersion not only of a conventional single mode fibre (SMF),with a D_(t)/s_(t) ratio equal to approximately 251.1 nm, but also ofother transmission optical fibres with a D_(t)/s_(t) ratio lower than150 nm as, for example, those listed in tables 1 and 3.

[0199]FIG. 8a illustrates the propagation delay (calculated with regardsto the propagation time at 1550 nm) with respect to the wavelength λalong an optical communication line 1 including 100 Km of transmissionoptical fibre 10 of the SMF type and 6.4 Km of compensating opticalfibre 12 according to the invention (having the values of d, Λ, L_(c),D_(c)/s_(c) and D_(c) as of Table 3).

[0200]FIG. 8b illustrates an enlarged detail of FIG. 8a, in a range ofwavelengths between 1500 and 1600 nm.

[0201] From this figure it can be noted how the maximum delayaccumulated (with regards to the propagation time at the wavelength of1550 nm) in the optical communication line according to the invention isonly of approximately 430 ps in a range of wavelength of 100 nm.

[0202] Furthermore, in the range of wavelength between 1530 and 1570 nm,the maximum delay accumulated with regards to the propagation time at awavelength of 1550 nm is only of approximately 60 ps.

[0203] The optical communication line 1 according to the invention is,therefore, efficiently compensated in terms of chromatic dispersion andalso in terms of chromatic dispersion slope, in a range of wavelengthsof approximately 100 nm.

[0204]FIG. 9 illustrates the residual dispersion coefficient D of theoptical communication line 1 comprising 100 Km of transmission opticalfibre 10 of the SMF type and 6.4 Km of compensating optical fibre 12according to the invention (with values of d, Λ, L_(c), D_(c)/s_(c) andD_(c) as per Table 3).

[0205] From the results of FIG. 9, the residual chromatic dispersioncoefficient D of such line appears to be approximately 4.7*10⁻⁵ps/(nm*Km) at 1550 nm, with a chromatic dispersion slope ofapproximately 0.00135 ps/(nm²*Km).

[0206] Furthermore, between 1500 and 1600 nm, the maximum variation ofthe residual chromatic dispersion coefficient D of the line is,approximately 0.16 ps/(nm*Km), while between 1530 and 1570 nm it is of0.055 ps/(nm*Km).

[0207] Considering that the dispersion typically tolerated in a WDMoptical communication system, with a transmission format of thenon-return to zero (NRZ) type at 40 Gbit/sec is of approximately 100ps/nm, the compensating optical fibre 12 according to the inventionallows to provide a WDM NRZ optical communication line, at 40 Gbit/sec,in the band of 1530-1570 nm, with a span length higher thanapproximately 1800 Km.

[0208] In order to compare the performances of a conventionalcompensating optical fibre with those of a compensating optical fibreaccording to the invention, the Applicant has compared the performancesof a compensating optical fibre produced by Lucent Technologies(described in the above-mentioned article by L. Gruner-Nielsen et al.,“Design and manufacture of dispersion compensating fibre forsimultaneous compensation of dispersion and dispersion slope”, OFC '99,Technical Digest WM13, pages 232-234)—with a W refractive index andsuitable to compensate the dispersion of a single mode transmissionoptical fibre (SMF)—with those of the compensating optical fibreaccording to the invention, having the values of d and Λ (d≅0.8 μm andΛ≅1 μm) corresponding, in Table 3, to a SMF transmission fibre.

[0209] Table 4 illustrates the values of D_(c), s_(c), residual s after100 Km of SMF transmission optical fibre and a suitable length ofcompensating fibre (L_(c)=D_(t)*L_(t)/D_(c)) and the maximum absolutevalue D_(max) of the residual chromatic dispersion coefficient in arange of 1500-1600 nm and in a range of 1530-1750 nm. TABLE 4 residualD_(max) D_(max) D_(c) s_(c) s ps/nm*Km ps/nm*Km Type of ps/ ps/ ps/1500-1600 1530-1570 fibre nm*Km nm²*Km nm²*Km nm nm Conven- −105.4 −0.331.1E⁻³ 0.5 0.087 tional Inven- −266.8 −1.04 6.5E⁻⁴ 0.13 0.029 tion

[0210] From the values of Table 4 we can see that the compensatingoptical fibre according to the invention is almost three times moreefficient than a conventional compensating optical fibre.

[0211] Furthermore, as already mentioned above, the compensating opticalfibre according to the invention can compensate for any type oftransmission optical fibre and not only a SMF transmission optical fibreas a conventional compensating optical fibre.

[0212] Table 5 illustrates the values of Λ, d, L_(c) achieved withrelations B, C and E of the invention for a value of d/Λ equal to 0.9 tocompensate the chromatic dispersion slope s_(t) as well as the chromaticdispersion coefficient D_(t) of the transmission optical fibre length10, in the case of length L_(t) equal to 100 Km's and in different casesin which it is made of a SMF, TW™, TW+™, TW RS™, LEAF, LEAF Enhanced andFreeLight™ optical fibre (the typical values of D_(t), s_(t) andD_(t)/s_(t) of these optical fibres are illustrated in Table 1).

[0213] Furthermore, Table 5 illustrates the values of the ratioD_(c)/s_(c) and of D_(c) achieved at 1550 nm, for a refractive index nequal to 1.45 and in correspondence with the values of d and Λ of Table5. TABLE 5 Type of Λ d L_(c) D_(c)/s_(c) D_(c) fibre (μm) (μm) (Km) (nm)ps/(nm*Km) SMF 0.97 0.87 4.78 256.5 −355.5 TW ™ 1.15 1.04 9.41 34 −25.5TW+ ™ 1.13 1.01 6.22 75.7 −64.3 TW RS ™ 1.07 0.96 3.91 140.7 −145.5 LEAF1.15 1.04 14.50 34 −25.5 LEAF Enh. 1.14 1.02 8.49 62.1 −50.6 FreeLight ™1.14 1.02 6.76 62.1 −50.6

[0214] By comparing the values of L_(c) of Table 5 achieved for a ratioof d/Λ equal to 0.9 with those of Table 3 achieved for a ratio of d/Λequal to 0.8, it can be noted how, generally, as the ratio d/Λ increasesthe efficiency in compensation of the compensating optical fibre length12 also increases.

[0215] In the case that the sole positive chromatic dispersioncoefficient D_(t) of the length of optical fibre transmission 10 is tobe compensated, the compensating optical fibre length 12 can bedesigned, according to the method of the invention, to effectivelycompensate such chromatic dispersion coefficient D_(t).

[0216] More in particular, in order that the compensating optical fibrelength 12 has, at a wavelength λ, a high value of negative chromaticdispersion coefficient D_(t), it must be designed in such a way that theparameters d and Λ satisfy the following relation:

−0.5≦d/Λ<1   (G) $\begin{matrix}{\Lambda = {{\frac{\lambda}{n}\left( \frac{1}{1 + {\frac{1}{2}\frac{d}{\Lambda}}} \right)} \pm {0.25\quad {µm}}}} & (H)\end{matrix}$

[0217] where n is the refractive index of the material making up thecore region 13 (and the cladding region 14 when it is made up of thesame material of the core region 13) of the compensating optical fibrelength 12.

[0218] The Applicant has verified that the relationship H is in fullagreement with the corresponding values of Λ that are achieved byresolving the Maxwell equations in a range of wavelengths between 1300and 1700 nm.

[0219] More in particular, the relation$\Lambda = {\frac{\lambda}{n}\left( \frac{1}{1 + {\frac{1}{2}\frac{d}{\Lambda}}} \right)}$

[0220] provides an excellent approximation (with a margin of error inthe order of a few nm's) of the value of Λ corresponding to a maximumnegative value of D_(c) around a wavelength of 1550 nm and for a valueof d/Λ of at least approximately 0.7

[0221] For example, considering

[0222] a wavelength λ of 1550 nm,

[0223] a ratio d/Λ equal to 0.8,

[0224] a refractive index n equal to 1.45 (equal to approximately therefractive index of silica at 1550 nm), the value of Λ which guaranteesthat the compensating optical fibre length 12 has a maximum negativevalue of the chromatic dispersion coefficient D_(c) is equalapproximately, according to the invention, to 0.76 μm.

[0225] The value of Λ thus found according to the method of theinvention is in full agreement with the results of FIG. 5 achieved byresolving the Maxwell equations.

[0226] Once the value of Λ has been chosen within such range, the valueof d can be determined by the relationship d/Λ=0.8.

[0227] According to an embodiment illustrated in FIG. 2, the opticalcommunication line 1 includes, besides the two lengths of optical fibre10 and 12 also an optical amplifier 11, located downstream thecompensating optical fibre length 12.

[0228] As illustrated in FIG. 6, the optical amplifier 11 includes anerbium doped active optical fibre length 15 and a pumping source 16 (forexample, a laser source) to pump the active optical fibre 15 at apumping wavelength λ_(p). The pumping source 16 is coupled to an inputend of the active optical fibre 15 and to the compensating optical fibrelength 12 by a wavelength selective coupler 17 (for example a fusedfibre coupler) in such a way that the signal and pumping light propagatetogether through the fibre 15.

[0229] However, according to the necessities of the system, the pumpingsource 16 can also be coupled to the output end of the active fibre 15(as indicated with a dotted line with 18) in such a way that the signaland pumping light propagate in opposite directions through the fibre 15.

[0230] Alternatively, each end of the fibre 15 can be coupled to arespective pumping source.

[0231] In the embodiment illustrated, the wavelength λ_(p) of thepumping signal is equal to approximately 980 nm.

[0232] The optical amplifier 11 described may optionally comprise morethan one stage of optical amplification.

[0233] Typically, according to a embodiment not illustrated, the opticalcommunication line 1 of the invention comprises a plurality oftransmission optical fibre lengths 10, a plurality of optical amplifiers11 interposed between one length and another of transmission opticalfibre 10 and at least one compensating optical fibre length 12 accordingto the invention to compensate at least in part the chromatic dispersionand/or the chromatic dispersion slope of the plurality of lengths oftransmission optical fibre 10.

[0234] Such compensating optical fibre length 12 can be located at thebeginning, at the end or within said optical communication line 1.Advantageously, it is inserted within the line 1 between onetransmission optical fibre length 10 and an optical amplifier 11.

[0235]FIG. 3 illustrates an optical communication system 20 according tothe invention comprising a transmitting station 22 to provide a signalat a signal wavelength λ, a receiving station 24 to receive such signal,and an optical communication line 1 according to the invention totransmit the signal from the transmitting station 22 to the receivingstation 24.

[0236] According to a preferred embodiment, the optical communicationsystem 20 is a WDM system.

[0237] In this case, the transmitting station 22 is a conventional WDMapparatus suitable to supply N optical signals with wavelengths λ1, λ2 .. . λN different from each other, and to multiply them in wavelengthsand to send them to the optical communication line 1.

[0238] Furthermore, the transmitting station 22 also comprises anoptical power amplifier (booster)—not illustrated—to amplify the WDMoptical signal before sending it along the line 1 (or a number ofoptical power amplifiers in parallel to amplify optical signalscomprised in different bands of wavelengths).

[0239] Such wavelengths λ1, λ2. . . λN are advantageously selectedwithin a range of wavelengths comprised between approximately 1500 nmand 1600 nm.

[0240] For example, the communication system 10 can be a WDM system with128 channels spaced apart from each other of 50 GHz and divided up intothree bands: 16 channels between 1529 and 1535 nm (first band); 48channels between 1541 and 1561 nm (second band) and 64 channels between1575 and 1602 nm (third band).

[0241] Said receiving station 24 comprises a conventional apparatussuitable to demultiplex said optical signals N and send them to anypossible subsequent stages of processing. Furthermore, said receivingstation 24 typically comprises also an optical pre-amplifier (notillustrated) suitable to bring the WDM optical signal to a level ofpower suitable to be received by the receiving apparatuses (or a numberof optical pre-amplifiers in parallel to amplify the optical signalscomprised in different bands of wavelengths).

[0242] Line 1 comprises a plurality of optical amplifiers 11, of thetype described with reference to FIG. 6, to amplify a signal coming froman upstream length of line, in which the signal has been attenuatedduring its propagation along it, and to send it to a downstream lengthof line.

[0243] Alternatively, instead of each optical amplifier 11, line 1 caninclude a number of optical amplifiers placed in parallel in order toamplify the optical signals comprised in different bands of wavelengths(for example, the first, second and third band mentioned above).

[0244] For example, system 20 can be a submarine optical communicationsystem, in which line 1 includes optical cables 1 ₁, 1 ₂, 1 ₃, . . . 1_(n) which connect respectively the transmitting station 22 to the firstamplifier 11, such amplifier 11 to the following and the last amplifier11 to the receiving station 24.

[0245] Each optical cable 1 ₁, 1 ₂, . . . 1 _(n) in comprises, forexample, a transmission optical fibre length 10 and a compensatingoptical fibre length 12 according to the invention.

[0246] Alternatively, each optical cable 1 ₁, 1 ₂, . . . 1 _(n)comprises a transmission optical fibre length 10 and the compensatingoptical fibre length 12 is inserted between the last optical cable 1_(n) and the receiving station 24 and/or only in some optical cables 1₁, 1 ₂, . . . 1 _(n) depending on the applications.

[0247] From the results illustrated in FIG. 8, the compensating opticalfibre length 12 can efficiently compensate the chromatic dispersion aswell as the chromatic dispersion slope of the lengths of transmissionoptical fibre 10 in a range of wavelengths between 1500 and 1600 nmwhich comprises the above-mentioned three transmission bands of the 128WDM channels.

1. An optical communication line comprising a transmission optical fibrelength (10) with, at a wavelength λ, a positive chromatic dispersionslope s_(t); a compensating optical fibre length (12), associated tosaid transmission optical fibre length (10), having a negative chromaticdispersion slope s_(c) suitable to compensate at least in part thepositive chromatic dispersion slope s_(t) of the transmission fibre,said compensating optical fibre (12) having a core region (13)surrounded by a cladding region (14), the cladding region (14) defininga first ring of holes, which substantially defines, around the coreregion (13), an annulus with an inner radius r1 and an outer radius r2,and at least one second ring of holes that surrounds the first ring ofholes, said holes running along the compensating optical fibre (12)longitudinally and being spaced apart from each other substantiallyaccording to a predefined pitch Λ, wherein a) the values of said innerradius r1 and said outer radius r2 are selected in such a way as tosubstantially satisfy the following relationship (L) r1≦λ/n≦r2  where nis the refractive index of the material making up the core region (13)of said compensating optical fibre length (12) b) the holes of saidfirst and said at least one second ring are substantially of the samediameter d, and c) the ratio d/Λ substantially satisfies the followingrelationship (A) 0.8≦d/Λ<1.
 2. An optical communication line (1)according to claim 1, wherein the ratio d/Λ substantially satisfies thefollowing relation 0.9≦d/Λ<1.
 3. An optical communication line (1)according to claims 1 or 2, wherein the value of the diameter d iscomprised between approximately 0.75 and 1.1 μm.
 4. An opticalcommunication line (1) according to any one of the claims from 1 to 3,wherein the value of Λ substantially satisfies the followingrelationship (C)${\frac{\lambda}{n}*\frac{1}{1 + {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}} \leq \Lambda \leq {\frac{\lambda}{n}*\frac{1}{1 - {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}}$


5. An optical communication line (1) according to claim 4, wherein thevalue of Λ substantially satisfies the following relationship (D)${\Lambda ({\mu m})} = {0.4 + {\frac{0.44}{d/\Lambda} \pm {0.02\quad {\mu m}}}}$

so that said compensating optical fibre length (12) has a negativechromatic dispersion slope s_(c) suitable to efficiently compensate thepositive chromatic dispersion slope s_(t) of said transmission opticalfibre length (10).
 6. An optical communication line (1) according to anyone of the claims from 1 to 4, wherein the transmission optical fibrelength (10) also has, at a wavelength λ, a positive chromatic dispersioncoefficient D_(t); and wherein the value of Λ substantially satisfiesthe following relationship (F)${\Lambda ({\mu m})} = {{\alpha*\frac{D_{t}}{s_{t}}} + {\beta \pm {0.02\quad {\mu m}\quad {where}}}}$${\alpha = {{{- 10^{- 4}}*\left( {{2.685*\frac{d}{\Lambda}} + 5.987} \right)\quad {and}\quad \beta} = {{3.4*\left( {\frac{d}{\Lambda} - 1} \right)^{3}} + 1.18}}}\quad$

 so that said compensating optical fibre length (12) has such achromatic dispersion coefficient D_(c) and such a chromatic dispersionslope s_(c) that the ratio D_(c)/s_(c) is substantially equal to theratio D_(t)/s_(t) in order to compensate both the chromatic dispersionslope and the chromatic dispersion of the transmission optical fibrelength (10).
 7. An optical communication system (20) comprising atransmitting station (22) suitable to provide an optical signal having asignal wavelength λ; a receiving station (24) suitable to receive saidoptical signal; an optical communication line (1), optically connectedto said transmitting station (22) and said receiving station (24) totransmit said optical signal, said line (1) comprising at least onetransmission optical fibre length (10), having at a wavelength λ apositive chromatic dispersion slope s_(t), and a compensating opticalfibre length (12), associated to said transmission optical fibre length(10), having a negative chromatic dispersion slope s_(c) suitable tocompensate at least in part the positive chromatic dispersion slopes_(t) of the transmission fibre (10), said compensating optical fibre(12) having a core region (13) surrounded by a cladding region (14), thecladding region (14) defining a first ring of holes, which substantiallydefines, around the core region (13), an annulus with an inner radius r1and an outer radius r2, and at least one second ring of holes whichsurrounds the first ring of holes, said holes running along thecompensating optical fibre (12) longitudinally and being spaced apartfrom each other substantially according to a predefined pitch Λ whereina) the values of said inner radius r1 and said outer radius r2 areselected in such a way as to satisfy the following relationship (L)r1≦λ/n≦r2  where n is the refractive index of the material making up thecore region (13) of said compensating optical fibre length (12) b) theholes of said first and said at least one second ring are substantiallyof the same diameter d, and c) the ratio d/Λ substantially satisfies thefollowing relationship (A) 0.8≦d/Λ<1.
 8. A method to design acompensating optical fibre (12) so that it has, at a predefinedwavelength λ, a negative chromatic dispersion slope s_(c), saidcompensating optical fibre (12) having a core region (13) surrounded bya cladding region (14), the cladding region (14) defining a first ringof holes, which substantially defines, around the core region (13), anannulus with an inner radius r1 and an outer radius r2, said holesrunning along the compensating optical fibre (12) longitudinally, havinga diameter d and being spaced apart from each other substantiallyaccording to a predefined pitch Λ, said method comprising the steps ofa) selecting a value of the ratio d/Λ through the following relationship(B) 0.5≦d/Λ<1, and b) selecting the values of said inner radius r1 andsaid outer radius r2 in such a way as to substantially satisfy thefollowing relationship (L) r1≦λ/n≦r2  where n is the refractive index ofthe material making up the core region (13) of said compensating opticalfibre (12).
 9. A method according to claim 8, characterised in that stepb) is carried out by selecting the value of Λ with the followingrelationship (C)${\frac{\lambda}{n}*\frac{1}{1 + {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}} \leq \Lambda \leq {\frac{\lambda}{n}*\frac{1}{1 - {\frac{1}{2}\left( \frac{d}{\Lambda} \right)}}}$

and in that, once the value of Λ has been selected, the value of d isdetermined through the value of the ratio d/Λ selected in step a).
 10. Amethod according to claim 9, characterised in that the step b) iscarried out by selecting the value of Λ using the following relationship(D)${\Lambda ({\mu m})} = {0.4 + {\frac{0.44}{d/\Lambda} \pm {0.02\quad {\mu m}}}}$

obtaining in this way an efficient compensating optical fibre (12). 11.A method according to claims 8 or 9, characterised in that, when acompensating optical fibre (12) is to be designed so that it has anegative chromatic dispersion coefficient D_(c) and is capable ofcompensating a positive chromatic dispersion coefficient D_(t) and apositive chromatic dispersion slope s_(t), the step b) is carried out byselecting the value of Λ in such a way as to satisfy the followingrelationship (E)${\Lambda ({\mu m})} = {{\alpha*\frac{D_{t}}{s_{t}}} + {\beta \pm {0.02\quad {\mu m}\quad {where}}}}$$\alpha = {{- 10^{- 4}}*\left( {{2.685*\frac{d}{\Lambda}} + 5.987} \right)}$$\beta = {{{3.14*\left( \frac{d}{\Lambda} \right)^{2}} - {5.162*\frac{d}{\Lambda}} + {3.3476\quad {for}\quad 0.5}} \leq {d/\Lambda} < 0.7}$$\beta = {{{{- 3.4}\left( {\frac{d}{\Lambda} - 1} \right)^{3}} + {1.18\quad {for}\quad 0.7}} \leq {d/\Lambda} < 1}$

in such a way that the chromatic dispersion coefficient D_(c) and thechromatic dispersion slope s_(c) of said compensating optical fibre (12)are such that the ratio D_(c)/s_(c) is substantially equal to the ratioD_(t)/s_(t).
 12. A method to determine the parameters d and Λ of acompensating optical fibre (12) so that it has, at a preselectedwavelength λ, a negative chromatic dispersion coefficient D_(c), saidcompensating optical fibre (12) having a core region (13) surrounded bya cladding region (14), the cladding region (14) defining a first ringof holes around the core region (13), said holes running along thecompensating optical fibre (12) longitudinally, having a diameter d andbeing spaced apart from each other substantially according to apredefined pitch Λ, said method comprising the steps of a)selecting avalue of the ratio d/Λ through the following relationship (G) 0.5≦d/Λ<1,b) selecting a value of Λ through the following relationship (H)$\Lambda = {{\frac{\lambda}{n}\left( \frac{1}{1 + {\frac{1}{2}\frac{d}{\Lambda}}} \right)} \pm {0.25\quad {\mu m}}}$

 where n is the refractive index of the material making up the coreregion (13) of said compensating optical fibre (12), and c) once thevalue of Λ has been selected, determining the value of d through thevalue of the ratio d/Λ selected in step a).
 13. A device forcompensating the chromatic dispersion and/or the chromatic dispersionslope comprising a compensating optical fibre length (12), comprising,in turn, a core region (13) surrounded by a cladding region (14), thecladding region (14) defining a first ring of holes, which substantiallydefines, around the core region (13), an annulus with an inner radius r1and an outer radius r2, and at least one second ring of holes thatsurrounds the first ring of holes, said holes running along thecompensating optical fibre (12) longitudinally and being spaced apartfrom each other substantially according to a predefined pitch Λ, whereina) the values of said inner radius r1 and said outer radius r2 are suchas to satisfy the following relationship (L) r1≦λ/n≦r2  where n is therefractive index of the material making up the core region (13) of saidcompensating optical fibre length (12) b) the holes of said first and ofsaid at least one second ring are substantially of the same diameter d,and c) the ratio d/Λ substantially satisfies the following ratio (A)0.8≦d/Λ<1.
 14. A device for compensating the chromatic dispersion and/orthe chromatic dispersion slope comprising a compensating optical fibre(12) comprising, in turn, a core region (13) surrounded by a claddingregion (14), the cladding region (14) defining a first ring of holesthat surrounds the core region (13) and at least one second ring ofholes that surrounds the first ring of holes, said holes running alongthe compensating optical fibre (12) longitudinally and being spacedapart from each other substantially according to a predefined pitch Λ,wherein the holes of said first and said at least one second ring aresubstantially of the same diameter d, the ratio d/Λ substantiallysatisfies the following relationship (A) 0.8≦d/Λ<1, and the value of Λis comprised between approximately 0.95 and 1.21 μm.